This thesis concerns optimization of structures considering various uncertainties. The overall objective is to find methods to create solutions that are optimal both in the sense of handling the typical load case and minimising the variability of the response, i.e. robust optimal designs. Traditionally optimized structures may show a tendency of being sensitive to small perturbations in the design or loading conditions, which of course are inevitable. To create robust designs, it is necessary to account for all conceivable variations (or at least the influencing ones) in the design process. The thesis is divided in two parts. The first part serves as a theoretical background to the second part, the two appended articles. This first part includes the concept of robust design, basic statistics, optimization theory and meta modelling. The first appended paper is an application of existing methods on a large industrial example problem. A sensitivity analysis is performed on a Scania truck cab subjected to impact loading in order to identify the most influencing variables on the crash responses. The second paper presents a new method that may be used in robust optimizations, that is, optimizations that account for variations and uncertainties. The method is demonstrated on both an analytical example and a Finite Element example of an aluminium extrusion subjected to axial crushing. / ROBDES

<p>This thesis concerns optimization of structures considering various uncertainties. The overall objective is to find methods to create solutions that are optimal both in the sense of handling the typical load case and minimising the variability of the response, i.e. robust optimal designs.</p><p>Traditionally optimized structures may show a tendency of being sensitive to small perturbations in the design or loading conditions, which of course are inevitable. To create robust designs, it is necessary to account for all conceivable variations (or at least the influencing ones) in the design process.</p><p>The thesis is divided in two parts. The first part serves as a theoretical background to the second part, the two appended articles. This first part includes the concept of robust design, basic statistics, optimization theory and meta modelling.</p><p>The first appended paper is an application of existing methods on a large industrial example problem. A sensitivity analysis is performed on a Scania truck cab subjected to impact loading in order to identify the most influencing variables on the crash responses.</p><p>The second paper presents a new method that may be used in robust optimizations, that is, optimizations that account for variations and uncertainties. The method is demonstrated on both an analytical example and a Finite Element example of an aluminium extrusion subjected to axial crushing.</p> / ROBDES

The distribution of liquid gazes (or cryogenic liquids) using bulks and tractors is a particular aspect of a fret distribution supply chain. Traditionally, these optimisation problems are treated under certainty assumptions. However, a large part of real world optimisation problems are subject to significant uncertainties due to noisy, approximated or unknown objective functions, data and/or environment parameters. In this research we investigate both robust and stochastic solutions. We study both an inventory routing problem (IRP) and a production planning and customer allocation problem. Thus, we present a robust methodology with an advanced scenario generation methodology. We show that with minimal cost increase, we can significantly reduce the impact of the outage on the supply chain. We also show how the solution generation used in this method can also be applied to the deterministic version of the problem to create an efficient GRASP and significantly improve the results of the existing algorithm. The production planning and customer allocation problem aims at making tactical decisions over a longer time horizon. We propose a single-period, two-stage stochastic model, where the first stage decisions represent the initial decisions taken for the entire period, and the second stage representing the recovery decision taken after an outage. We aim at making a tool that can be used both for decision making and supply chain analysis. Therefore, we not only present the optimized solution, but also key performance indicators. We show on multiple real-life test cases that it isoften possible to find solutions where a plant outage has only a minimal impact.

Health care, and especially access to health care, has always been a critical metric for countries. In 2017, South Africa spent 9% of its GDP on health care. Despite the GDP health care allocation being 5% higher than recommended by the World Health Organisation for a country of its socio-economic status, South Africa's health status is poor compared to similar countries. In 1994, South Africa implemented a health care policy to make health care accessible to all South Africans. A primary health care facility within 5km of the place of residence is deemed accessible. There is still a significant gap between the actual and desired accessibility, especially for the lower-income communities. There is a need to improve access to public health care for all South Africans. Cost-effective and sustainable solutions are required to solve this problem. Therefore, an opportunity was identified to investigate the location of low-cost container clinics in lower-income communities. This report uses robust optimisation and goal programming to find robust sites for cost-effective container clinics over multiple years in an uncertain environment using multiple future city development scenarios. The study area of the report includes three metro municipalities (City of Tshwane, City of Johannesburg, and City of Ekurhuleni) in Gauteng, South Africa. Three future development scenarios were created for this study using a synthetic population and urban growth simulation model developed by the CSIR. The model provided the population distribution from 2018 to 2030 for all three of the scenarios. The simulation model provides household attribute tables as an output. Household attributes that have a causal relationship with health care demand were investigated during the literature review. Based on the literature and the available household attributes, four attributes were selected to forecast the health care demand. The four attributes are household income, the number of children in the household, the household size, and the nearest clinic's distance. Using associative forecasting, the primary health care demand was forecasted from 2018 to 2030. These forecasts were used as input into the facility location models. A p-median facility location model was developed and implemented in Python. Since facility location problems are classified as NP-hard problems, heuristics and metaheuristics were investigated to speed up the problem solving. A GA selected as the metaheuristic be used to determine a suitable configuration of facilities for each scenario. The model determined good locations of clinics from a set of candidate locations. A good year to open each clinic is also determined by the model. These decisions are made by minimising three variables: total distances travelled by the households to their nearest clinics, the total distance from the selected distribution centre to the open clinics and the total building cost. An accessibility target of 90% was added to the model to ensure that at least 90% of the households are within 5km of the nearest clinic within the first five years. In these models, operating costs were not included. Therefore all the results are skewed, with most of the clinics being opened in the first year when it is the cheapest since there is no penalty for opening a clinic before it is needed — the exclusion of operating costs is a shortcoming to address in future work. A goal programming model was developed with the variables of the individual scenarios as the goals. The goal programming model was implemented in Python and used to determine a robust configuration of where and in what year to open container clinics. A difference of 25% was set as the upper limit for the difference between the robust configuration variables and the good or acceptable variables for the individual scenarios as the scenarios investigated are very different. This ensured that the robust solution would perform well for any of the three scenarios. The model was able to find locations that provided a relatively good solution to all the scenarios. This came with a cost increase, but that is a trade-off that must be made when dealing with uncertainty. This model is a proof of concept to bridge the gap between urban planning with multiple development scenarios and facility location, more specifically robust facility location. The biggest rendement was achieved by constructing and placing the container clinics in the shortest space of time because the 90% accessibility requirement can be addressed cost-effectively without an operating cost penalty ― this is unfortunately not possible in reality due to budget constraints. An accessibility analysis was conducted to investigate the impact of the accessibility percentage on the variable values and to test the model in a scenario closer resembling the real world by adding a budget constraint. The time limit of the accessibility requirement was removed. In this case, a gradual improvement in the accessibility over the 12 years was observed due to the gradual opening of clinics over the years. Based on the analyses results, it was concluded that the model is sensitive to changes in parameters and that the model can be used for different scenarios. / Dissertation (MEng (Industrial Engineering))--University of Pretoria, 2021. / Industrial and Systems Engineering / MEng (Industrial Engineering) / Unrestricted

Substantial anthropogenic change of the Earth’s climate is modifying patterns of rainfall, river flow, glacial melt and groundwater recharge rates across the planet, undermining many of the stationarity assumptions upon which water resources infrastructure has been historically managed. This hydrological uncertainty is creating a potentially vast range of possible futures that could threaten the dependability of vital regional water supplies. This, combined with increased urbanisation and rapidly growing regional populations, is putting pressures on finite water resources. One of the greatest international challenges facing decision makers in the water industry is the increasing influences of these “deep” climate change and population growth uncertainties affecting the long-term balance of supply and demand and necessitating the need for adaptive action. Water companies and utilities worldwide are now under pressure to modernise their management frameworks and approaches to decision making in order to identify more sustainable and cost-effective water management adaptations that are reliable in the face of uncertainty. The aim of this thesis is to compare and contrast a range of existing Decision Making Methods (DMMs) for possible application to Water Resources Management (WRM) problems, critically analyse on real-life case studies their suitability for handling uncertainties relating to climate change and population growth and then use the knowledge generated this way to develop a new, resilience-based WRM planning methodology. This involves a critical evaluation of the advantages and disadvantages of a range of methods and metrics developed to improve on current engineering practice, to ultimately compile a list of suitable recommendations for a future framework for WRM adaptation planning under deep uncertainty. This thesis contributes to the growing vital research and literature in this area in several distinct ways. Firstly, it qualitatively reviews a range of DMMs for potential application to WRM adaptation problems using a set of developed criteria. Secondly, it quantitatively assesses two promising and contrasting DMMs on two suitable real-world case studies to compare highlighted aspects derived from the qualitative review and evaluate the adaptation outputs on a practical engineering level. Thirdly, it develops and reviews a range of new potential performance metrics that could be used to quantitatively define system resilience to help answer the water industries question of how best to build in more resilience in future water resource adaptation planning. This leads to the creation and testing of a novel resilience driven methodology for optimal water resource planning, combining optimal aspects derived from the quantitative case study work with the optimal metric derived from the resilience metric investigation. Ultimately, based on the results obtained, a list of suitable recommendations is compiled on how to improve the existing methodologies for future WRM planning under deep uncertainty. These recommendations include the incorporation of more complex simulation models into the planning process, utilisation of multi-objective optimisation algorithms, improved uncertainty characterisation and assessments, an explicit robustness examination and the incorporation of additional performance metrics to increase the clarity of the strategy assessment process.

Dans cette thèse, nous nous intéressons à des chaînes logistiques dont les acteurs de la chaîne sont des entités décisionnelles indépendantes. Plus précisément, notre cadre d’étude sera un "maillon" d’une chaîne logistique (relation client fournisseur) dont les acteurs (le client et le fournisseur) sont des entités décisionnelles indépendantes qui souhaitent mettre en place des processus de planification coopératifs en présence d’incertitude, sachant que le client fabriques des produits à la commande et le fournisseur sur stock. Dans ce contexte, la contribution majeure visée par nos travaux est l’intégration des connaissances imparfaites sur les données (date du besoin en composants, quantité nécessaire…etc.) afin de calculer le plan d’approvisionnement plus robuste (plan minimisant l’impact de l’incertitude). L’intégration des imperfections repose sur l’utilisation de la théorie des possibilités. Une fois le modèle de représentation des données imparfaites réalisé, nous proposons des méthodes de calcul de plan d’approvisionnement utilisant les informations supplémentaires grâce à la représentation des imperfections. / In this thesis, we focus on supply chain where the actors are independent entities. More precisely, ours interests are on point-to-point (customer/supplier) relationships where the actors (the customer and the supplier) are independent entities which want to set up collaborative planning process under uncertainty, such that the customer produces to orders and the supplier produces to stock. In this context, the major contribution of the thesis is the integration of ill-known data (date of requirement, required quantities ...etc.) to calculate a robust procurement plan (plan which minimize the impact of uncertainty). We used the possibility theory to model those uncertainties. After the model of ill-known data proposed, we present a set of methods to compute a procurement plan using the additional information (information on the uncertainty).

La distribution de liquide cryogénique en « vrac », ou par camions citernes, est un cas particulier des problèmes d’optimisation logistique. Ces problèmes d’optimisation de chaines logistiques et/ou de transport sont habituellement traités sous l’hypothèse que les données sont connues à l’avance et certaines. Or, la majorité des problèmes d’optimisation industriels se placent dans un contexte incertain. Mes travaux de recherche s’intéressent aussi bien aux méthodes d’optimisation robuste que stochastiques.Mes travaux portent sur deux problèmes distincts. Le premier est un problème de tournées de véhicules avec gestion des stocks. Je propose une méthodologie basée sur les méthodes d’optimisation robuste, représentant les pannes par des scénarios. Je montre qu’il est possible de trouver des solutions qui réduisent de manière significative l’impact des pannes d’usine sur la distribution. Je montre aussi comment la méthode proposée peut aussi être appliquée à la version déterministe du problème en utilisant la méthode GRASP, et ainsi améliorer significativement les résultats obtenu par l’algorithme en place. Le deuxième problème étudié concerne la planification de la production et d’affectation les clients. Je modélise ce problème à l’aide de la technique d’optimisation stochastique avec recours. Le problème maître prend les décisions avant qu’une panne ce produise, tandis que les problèmes esclaves optimisent le retour à la normale après la panne. Le but est de minimiser le coût de la chaîne logistique. Les résultats présentés contiennent non seulement la solution optimale au problème stochastique, mais aussi des indicateurs clés de performance. Je montre qu’il est possible de trouver des solutions ou les pannes n’ont qu’un impact mineur. / The distribution of liquid gazes (or cryogenic liquids) using bulks and tractors is a particular aspect of a fret distribution supply chain. Traditionally, these optimisation problems are treated under certainty assumptions. However, a large part of real world optimisation problems are subject to significant uncertainties due to noisy, approximated or unknown objective functions, data and/or environment parameters. In this research we investigate both robust and stochastic solutions. We study both an inventory routing problem (IRP) and a production planning and customer allocation problem. Thus, we present a robust methodology with an advanced scenario generation methodology. We show that with minimal cost increase, we can significantly reduce the impact of the outage on the supply chain. We also show how the solution generation used in this method can also be applied to the deterministic version of the problem to create an efficient GRASP and significantly improve the results of the existing algorithm. The production planning and customer allocation problem aims at making tactical decisions over a longer time horizon. We propose a single-period, two-stage stochastic model, where the first stage decisions represent the initial decisions taken for the entire period, and the second stage representing the recovery decision taken after an outage. We aim at making a tool that can be used both for decision making and supply chain analysis. Therefore, we not only present the optimized solution, but also key performance indicators. We show on multiple real-life test cases that it isoften possible to find solutions where a plant outage has only a minimal impact.

In an air defence scenario decisions need to be taken with extreme precision and under high pressure. These decisions becomes even more challenging when the aircraft in question need to function as a team and coordinate their effort. Because of the difficulty of the task, and the amount of information that needs to be rapidly processed, fighter pilots can benefit greatly from computer-assisted decision making.  In this thesis this kind of decentralised multi-agent coordination problem is studied and mission assignment models, based on robust and stochastic optimisation, are evaluated. Since the information obtained by aircraft sensors often suffer from a notable amount of noise and the scenario state therefore is uncertain, a Poisson multi-Bernoulli mixture filter is implemented in order to model these noisy measurements and keep track of potential adversaries. The study finds that the filter used was more than capable of handling the scenario uncertainties and provided valuable task information to the mission assignment models. However, the preliminary robust optimisation models based entirely on the positional uncertainty of the adversaries were not sophisticated enough for such a complex coordination problem, indicating that further research is needed in this area.

Ce travail porte sur l’optimisation robuste des lignes de production au stade de la conception. La conception de telles lignes peut être interprétée comme un problème d’optimisation consistant à rechercher une configuration optimisant des objectifs individuels et à respecter les contraintes technologiques et économiques. Nous considérons deux types de lignes de production : l’assemblage et le transfert. Le premier peut être représenté comme un ensemble de stations ordonnées linéairement où les tâches sont exécutées de manière séquentielle. Le second type de ligne est constitué de machines de transfert comprenant plusieurs têtes multibroches. Toutes les tâches d’une même tête sont exécutées simultanément, tandis que les outils d’une machine fonctionnent en mode séquentiel. Nous décrivons différentes approches permettant de modéliser l’incertitude des données dans les problèmes d’équilibrage de ligne. Notre objectif est d’identifier les approches les mieux adaptées au contexte de la conception. En particulier, l’attention se concentre sur l’approche robuste. Nous proposons un nouveau critère d’optimisation basé sur le rayon de stabilité d’une solution réalisable. Ensuite, des formulations robustes sont présentées pour la conception des lignes d’assemblage et de transfert lorsque le temps de traitement des tâches est sujet à des incertitudes. Nous développons également des méthodes heuristiques dont les résultats sont utilisés pour renforcer les modèles mathématiques. Enfin, une nouvelle méthode de résolution hybride est élaborée pour résoudre différentes variantes des problèmes de maximisation du rayon de stabilité. / This work deals with a robust optimisation of production lines at the design stage. The design of such lines can be interpreted as an optimisation problem that consists in finding a configuration optimising individual objectives and respecting technological and economic constraints. We conside rtwo types of production lines: assembly and transfer lines. The first one can be represented as a set of linearly ordered stations where the tasks are executed sequentially. The second one is composed of transfer machines, including several multispindle heads. All tasks within a single head are executed simultaneously, while tools on a machine work in a sequential mode. We describe different approaches for modelling the uncertainty of data in line balancing problems. Our objective is to identify the approaches that best fit the context of the design. In particular, the attention concentrates on the robust approach. We propose a new optimisation criterion based on the stability radius of a feasible solution. Then, robust formulations are presented for the design of the assembly and transfer lines under variations of task processing times. We also develop heuristic methods whose results are used to improve mathematical models. Finally, a new hybrid resolution method is elaborated to solve different variants of the stability radius maximisation.

Les travaux présentés dans cette thèse, qui s’inscrivent dans le cadre du projet franco-allemand DSS_Evac_Logistic, visent à proposer des méthodes permettant de calculer des plans d’évacuation macroscopiques d’une ville lors d’une catastrophe majeure. Deux problèmes d’évacuations sont considérés dans cette thèse : le problème d’évacuation par bus et le problème d’évacuation par bus et voitures. Le problème d’évacuation par bus a pour objectif de définir un plan d’évacuation afin de mettre à l’abri les évacués. Dans cette thèse, nous nous sommes intéressés à l’étude de trois versions du problème d’évacuation par bus. La première version est monocritère où nous cherchons à minimiser la date de fin d’évacuation. Puis, dans le second problème et afin d’assurer la sécurité des évacués, nous avons considéré une version bicritère qui généralise le cas monocritère, en incluant le risque encouru lors de l’évacuation des personnes. Les deux critères à minimiser sont la date de fin d’évacuation et le risque. La troisième version est une version robuste bicritère qui permet d’appréhender l’incertitude sur les données. Le but est de minimiser à la fois la date de fin d’évacuation et les modifications apportées sur une solution, de sorte qu’elle soit réalisable pour n’importe quel scénario de données. Pour résoudre ces problèmes d’évacuation par bus, nous avons proposé des méthodes exactes et des méthodes heuristiques. / The work presented in this thesis, which is a part of the Franco-German project DSS_Evac_Logistic, aims at proposing methods to calculate macroscopic evacuation plans for mid-size towns after a tremendous disaster. Two evacuation problems have been tackled in this thesis : the bus evacuation problem and bus-and-vehicle evacuation problem. The bus evacuation problem aims at calculating an evacuation plan to relocate evacuees outside the endangered area. In this thesis, we consider three versions of the bus evacuation problem. The first one is a monocriterion problem, where the objective is to minimize the maximum evacuation time. In order to guarantee the safety of evacuees, we have considered a bicriteria problem, which is a generalization of the monocriterion version, in which we take into consideration the risk exposure of the evacuees. Consequently, the bicriteria problem is solved by minimizing the total evacuation time and the risk. The third version is a bicriteria robust version because most of the planning data is subject to uncertainty. The goal is to minimize both the evacuation time and the vulnerability of the schedule that is subject to different evacuation circumstances. To solve all the versions of the bus evacuation problem, we have developed exact solutions based on mathematical formulation to address small instances and heuristic solutions to deal with larger instances.